I have never done anything "useful". No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.
G. H. Hardy was born on 7 February 1877, in Cranleigh, Surrey, England, into a teaching family. His father was Bursar and Art Master at Cranleigh School; his mother had been a senior mistress at Lincoln Training College for teachers. Both parents were mathematically inclined.
After schooling at Cranleigh, Hardy was awarded a scholarship to Winchester College for his mathematical work. In 1896 he entered Trinity College, Cambridge. After only two years of preparation under his coach, Robert Alfred Herman, Hardy was fourth in the Mathematics Tripos examination. Years later, he sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end. While at university, Hardy joined the Cambridge Apostles, an elite, intellectual secret society.
As the most important influence Hardy cites the self-study of Cours d'analyse de l'École Polytechnique by the French Mathematician Camille Jordan, through which he became acquainted with the more precise mathematics tradition in continental Europe. In 1900 he passed part II of the Tripos and was awarded a fellowship. In 1903 he earned his M.A., which was the highest academic degree at English universities at that time. From 1906 onward he held the position of a lecturer where teaching six hours per week left him time for research. In 1919 he left Cambridge to take the Savilian Chair of Geometry (and thus become a Fellow of New College) at Oxford in the aftermath of the Bertrand Russell affair during World War I. Hardy spent the academic year 1928–1929 at Princeton in an academic exchange with Oswald Veblen, who spent the year at Oxford. Hardy gave the Josiah Willards Gibbs lecture for 1928. Hardy left Oxford and returned to Cambridge in 1931, where he was Sadleirian Professor until 1942.
From 1911 he collaborated with John Edensor Littlewood, in extensive work in mathematical analysis and analytic number theory. This (along with much else) led to quantitative progress on the Waring's Problem, as part of the Hardy–Littlewood circle method, as it became known. In prime number theory, they proved results and some notable conditional results. This was a major factor in the development of number theory as a system of conjectures; examples are the first and second Hardy–Littlewood conjectures. Hardy's collaboration with Littlewood is among the most successful and famous collaborations in mathematical history. In a 1947 lecture, the Danish Mathematician Harald Bohr reported a colleague as saying, "Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood."
Starting in 1914, Hardy was the mentor of the Indian Mathematician Srinivasa Ramanujan, a relationship that has become celebrated. Hardy almost immediately recognised Ramanujan's extraordinary albeit untutored brilliance, and Hardy and Ramanujan became close collaborators. In an interview by Paul Erdős, when Hardy was asked what his greatest contribution to mathematics was, Hardy unhesitatingly replied that it was the discovery of Ramanujan. He called their collaboration "the one romantic incident in my life."
He was at times politically involved, if not an Activist. He took part in the Union of Democratic Control during World War I, and For Intellectual Liberty in the late 1930s.
G. H. Hardy is usually known by those outside the field of mathematics for his essay from 1940 on the aesthetics of mathematics, A Mathematician's Apology, which is often considered one of the best insights into the mind of a working Mathematician written for the layman.
Moreover, Hardy deliberately pointed out in his Apology that mathematicians generally do not "glory in the uselessness of their work," but rather – because science can be used for evil ends as well as good – "mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean." Hardy also rejected as a "delusion" the belief that the difference between pure and applied mathematics had anything to do with their utility. Hardy regards as "pure" the kinds of mathematics that are independent of the physical world, but also considers some "applied" mathematicians, such as the physicists Maxwell and Einstein, to be among the "real" mathematicians, whose work "has permanent aesthetic value" and "is eternal because the best of it may, like the best literature, continue to cause intense emotional satisfaction to thousands of people after thousands of years." Although he admitted that what he called "real" mathematics may someday become useful, he asserted that, at the time in which the Apology was written, only the "dull and elementary parts" of either pure or applied mathematics could "work for good or ill."
Hardy is a key character, played by Jeremy Irons, in the 2015 movie The Man Who Knew Infinity, based on the biography of Ramanujan with the same title. Hardy is a major character in David Leavitt's fictive biography, The Indian Clerk (2007), which depicts his Cambridge years and his relationship with John Edensor Littlewood and Ramanujan. Hardy is a secondary character in Uncle Petros and Goldbach's Conjecture (1992), a mathematics novel by Apostolos Doxiadis.
